Add the coconut milk, tomatoes, sugar, and salt, and bring to a boil. Reduce the heat to a simmer and cook for 10 minutes.

Add the potatoes and cook for 15 to 20 minutes, until the potatoes are just fork-tender.

Add the remaining vegetables and chickpeas. Stir well to combine, cover, and reduce the heat to medium-low. Cook, stirring only occasionally, until the vegetables are tender but not falling apart, 40 minutes to 1 hour.